# The first and the last term of an A.P. are 8 and 350 respectively. If its common difference is 9, how many terms are there and what is their sum?

**Given:** An A.P. with first term a=8 and last term l=350 and the common difference d=9

**To do:** To find the numbers of the terms in the given A.P. and the sum of its terms also.

**Solution:**

As known that $l=a+( n-1) d$ in an A.P.

On substituting $l=350,\ a=8\ and\ d=9$ as given

$350=8+( n-1) 9$

$\Rightarrow n-1=\frac{350-8}{9}={342}{9}=38$

$\Rightarrow n=38+1=39$

And we know that the sum of n terms in an A.P.,

$S_{n}=\frac{n}{2} \ ( a+l)$

$=\frac{39}{2}( 8+350)$ $( on\ substituting\ the\ values\ of\ n,\ a\ and\ l)$

$=6981$

Hence, the given A.P. has 39 terms and sum of its all terms is 6981.

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